Exploring Relationships: Measures of Association

1. Exploring Relationships: Measures of Association Research Methods for Public Administrators Dr. Gail Johnson Dr. G. Johnson, www.ResearchDemystified.org

2. Exploring Linear Relationships • Researchers use crosstabs and comparison of means between two variables to see if there is a relationship • If we see some differences that suggest there is a relationship, the next steps is to determine how strong it is Dr. G. Johnson, www.ResearchDemystified.org

3. Direction of Relationship Revisited • Plus sign: direct relationship • Both variables change in the same direction • Example: as driving speed increases, death rate goes up Dr. G. Johnson, www.ResearchDemystified.org

4. Direction of Relationship Revisited • Minus sign: inverse relationship • Both variable change but in the opposite direction • Example:as age increases, health status decreases Dr. G. Johnson, www.ResearchDemystified.org

5. Measures of Association • How strong is the association? • Several different measures of association • Some measures of association range from 0 to 1 • Others range from minus1 to plus 1 Dr. G. Johnson, www.ResearchDemystified.org

6. How To Interpret Measures of Association • Measures of Association get interpreted in a similar way: • Perfect Relationship = 1 • Closer to 1: strong relationship • .5 moderate/strong • Closer to 0: no relationship • .2 some/slight Dr. G. Johnson, www.ResearchDemystified.org

7. How To Interpret Measures of Association • Interpreting measures of association that have a minus sign: • Minus sign indicates an inverse relationship (meaning as one variable goes up, the other goes down) • As age increases, memory decreases • For example, -.9 is a very strong relationship (almost perfect relationship because it is close to 1), but it is an inverse relationship because it has a minus sign Dr. G. Johnson, www.ResearchDemystified.org

8. Level Of Data: Common Measures of Association: • Nominal Data • Cramers V and Phi • Ordinal Data • Kendall’s Tau b and Tau c • Ordinal with interval/ratio data • Spearman’s Rho • Interval/Ratio data • Person’s r Dr. G. Johnson, www.ResearchDemystified.org

9. Gender and Attitude About Death Penalty: Revisited Dr. G. Johnson, www.ResearchDemystified.org

10. Gender and Attitude About the Death Penalty • The computer using SPSS provided these Measures of Association for the data on gender and attitude on the death penalty—expressed as the “Value” Value Phi .191 Cramer's V .191 • Interpretation: There is some difference in support of death penalty based on gender but it is a weak (fairly close to zero). Dr. G. Johnson, www.ResearchDemystified.org

11. Men Women Full time 64% 40% Part-time 7 13 Not working (school, unemployed, retired) 26 22 Keeping House 1 23 Other 2 2 Total 100% n=641 100% n=859 Gender differences in employment status? Dr. G. Johnson, www.ResearchDemystified.org

12. Gender Differences in Employment Status? • Interpretation of Percent Distribution: Yes, there are some differences based on gender. Sixty-four percent of the men reported working full time compared to 40% of the women. On the other hand, 23% of the women reported keeping house as compared to 1% of the men Measure of Association: Cramer’s V = .354 • Interpretation: It is a moderate or moderately strong relationship between gender and employment status Dr. G. Johnson, www.ResearchDemystified.org

13. STRONGLY AGREE AGREE DISAGREE STRONGLY DISAGREE Less than HS 25% 55% 15% 5% 100% High school 26% 49% 19% 6% 100% Junior college 26% 48% 16% 10% 100% Bachelor 12% 52% 29% 7% 100% Graduate 15% 49% 23% 12% 100% Total 23% 51% 20% 7% N=997 Views on Spanking: Related to Education Level? Dr. G. Johnson, www.ResearchDemystified.org

14. Attitudes about Spanking: Does education make a difference? Attitudes and Education are ordinal variables and the computer provides this measures of association: Tau C= .095 Interpretation? Dr. G. Johnson, www.ResearchDemystified.org

15. Highest Degree Mean N Less than HS $18,021 249 High school diploma 33,188 704 Associate degree 41,129 87 Bachelor degree 49,034 216 Graduate degree 62,275 108 Total $35,738 1364 Do People With Higher Degrees Earn More? Dr. G. Johnson, www.ResearchDemystified.org

16. Do People With Higher Degrees Earn More? • Hypothesis: people with higher degrees will earn more • Education is the independent variable: we think it explains differences in earnings. • Earnings is the dependent variable • Education level is an ordinal scale (even though it looks nominal-there is an order to it) • Earnings are ratio level data • Measure of Association: Spearman’s Rho Dr. G. Johnson, www.ResearchDemystified.org

17. Do People With Higher Degrees Earn More? • The computer crunches the numbers and states that Spearman’s Rho is .480 • Interpretation? Dr. G. Johnson, www.ResearchDemystified.org

18. Pearson’s r • Also called Pearson product-moment correlation coefficient is a measure of the correlation between two interval/ratio-level variables • It gives a measure that is between plus 1 and minus one. • The closer to zero, the weaker the relationship Dr. G. Johnson, www.ResearchDemystified.org

19. Correlation In The News • PEW Report: • What is the relationship between unemployment and Presidential approval ratings? • Using opinion data from the Gallup Polls and unemployment rates from census, PEW tried to determine the extent to which changes in unemployment rates correlated with citizens’ approval ratings of Presidents between 1980 and 2009. Dr. G. Johnson, www.ResearchDemystified.org

20. Left Side of Scale: Disapproval RatesRight Side of Scale: Unemployment Rates Dr. G. Johnson, www.ResearchDemystified.org

21. PEW Explains Correlation Coefficients The correlation coefficients shown in the next table measure the degree to which unemployment rates and presidential disapproval ratings “varied together over the past 30 years (coefficient of 1 or –1 indicating a totally positive or totally negative correspondence between two variables, a zero coefficient indicating no relationship at all). PEW: “It’s All About the Jobs Except When It Is Not,” January 26, 2010. Pew Research Center for the People & the Press http://pewresearch.org/pubs/1476/unemployment-presidential-approval-ratings-1981-2009-reagan-obama Dr. G. Johnson, www.ResearchDemystified.org

22. Correlation Coefficients Dr. G. Johnson, www.ResearchDemystified.org

23. Discussion: • Reagan’s first term and Obama’s first year show a high correlation: as unemployment rates went up, so did their disapproval ratings • But the trend lines for both are not perfectly matched • What other factors besides unemployment might affect disapproval ratings of Clinton and Bush? Dr. G. Johnson, www.ResearchDemystified.org

24. Relationships • When looking at relationships, a central question is: how strong is the relationship? • When presenting relationship data, researchers should provide the measures of association so the readers can make their own decision about the strength of the relationship. • Remember: it is rare to get high correlations or measures of association—especially in the social sciences. Dr. G. Johnson, www.ResearchDemystified.org

25. Relationships • Correlation does not mean the variables are in a cause-effect relationship. • Yes, good researchers begin by exploring a possible relationship and then “control for stuff” to see if the relationship disappears or if a relationship gets stronger under different scenarios. • Statistical controls is an effective technique to eliminate rival explanations but is not as strong as the classic experimental design. Dr. G. Johnson, www.ResearchDemystified.org

26. Creative Commons • This powerpoint is meant to be used and shared with attribution • Please provide feedback • If you make changes, please share freely and send me a copy of changes: • Johnsong62@gmail.com • Visit www.creativecommons.org for more information Dr. G. Johnson, www.ResearchDemystified.org